| Dynamic rupture propagation is very complex, which is controlled by many factors, such as complex fault geometries, complex medium and inhomogeneous stress distribution and so on. Further analyzing and discussing the influences of these factors on the rupture propagation is helpful for us to understand the physical mechanism of rupture initiation, propagation and cessation. It provides more reasonable explanations for the strong ground motion character as well. As a more applicable method for dynamic rupture propagation modeling, boundary integral equation method is utilized in this study. It has special advantages in dealing with complex fault geometries. Therefore, the purpose of the study is to discuss the important effects of the above factors on the rupture process based on the boundary integral equation method.To attain the goal, the works done in the paper are as follows.Earthquakes seldom rupture along the single planar faults. Instead, geometric complexities, including fault bends, branches and step overs, affect the rupture process, nucleation and arrest. In order to understand the influences of nonplanar fault geometry on the earthquake rupture, dynamic numerical simulation provides a new insight.First of all, starting from representative theorem, a basic boundary integral equation describing the relationship between stress and slip is obtained. And due to the two-order space derivation of the Green’s function, there is a difficulty in the hyper-singularity. To solve the problem, we resorted to wave motion equation and integration by part technique. Secondly, the discretization of the boundary integral equation is essential to obtain a more applicable equation for simulation. And for the fault discretization, we adopted the triangular meshes, which is seldom used in dealing with the similar problems with boundary integral equation method. Finally, after the regularization and discretization, the equation for numerical simulation is constructed.Dynamic rupture modeling, in essence, is a process of building equation and solve it with appropriate initial and boundary conditions. Friction criterion is one of the key points controlling the rupture initiation, propagation and cessation, and there are many friction laws commonly used in seismic source dynamics. After establishing the equation, we developed the simulation program in FORTRAN language to simulate the dynamic rupture propagation in full space. By contrast with typical numerical examples, the validation of the program was verified. Then, amount of numerical simulation experiments were done to retrieve the rupture phase diagram in full space. Finally, we built planar fault model, curve fault models and branch fault models to discuss the important influences of complex fault geometries on the dynamic rupture propagation.To understand the significant impacts of free surface and inhomogeneous stress distribution on the dynamic rupture propagation, the spontaneous seismic source dynamics in half space was carried out. And in terms of the key half Green’s function calculation, the directive wave was decomposed from reflective and refraction wave. For the Green’s function of the former, the Green’s function in full space was adopted. Whereas, that of the latter was calculated with an algorithm in half space. Thereby, the integration kernel was retrieved. By comparison with the kernels in full space and half space, it can be found that the existence of free surface indeed had significant effects on the dynamic rupture process. The problems in half space were further degenerated to that in full space, to verify the accuracy of the dynamic parameters calculation. After the examination, the rupture diagrams along the strike and dip direction were obtained. To achieve the ultimate goal, various models with different fault buried depth, dip angles and inhomogeneous stress distribution were built to study the influences of free surface. By applying the theories into practice, the dynamic rupture process of the 2010 Qinghai Mw7.1 earthquake was simulated.After detailed analysis, the general knowledge was retrieved.The dynamic rupture propagation behavior was controlled by many factors, such as the initial stress in and outside of the asperity, the critical slip-weakening distance, and the radius of asperities, etc. Even though the simple planar fault, the propagation was different with the parameters. By analyzing the influences of the parameters, the rupture diagram in full space was constructed. For the strike-slip fault, the dynamic rupture had three kinds:self-arresting, sub-shear rupture and super-shear rupture. While for the dip slip fault, only two forms existed without super-shear rupture phenomenon.For a simple planar fault, spontaneous rupture propagation initiates from a given circular asperity and then propagated bilaterally. And a bump of slip distribution near the center of the fault was the most significant feature of the fault that starts from an initial asperity. In addition, a curved fault was considered and find that a small inclination angle does not have significant effects on the rupture propagation. The rupture still could expand symmetrically and bilaterally beyond a bend. However, a large inclination angle might cause the rupture to propagate asymmetrically. The bend fault with big inclination angle could hinder or stop the rupture propagation, and could be regarded as geometric barrier. To the branch fault, when the angle between the main fault and the branch faults was small, the rupture propagated along the branch fault not the main fault. On the contrary, the rupture propagated both on the main fault and the branch fault. However, due to the energy dissipation, the total slip on both faults were small. That is to say, the local complex fault geometries or nonplanar fault structures played important roles in the earthquake initiation and rupture propagation.In half space, the existence of free surface, fault depth, dip angle and initial stress distribution all have great impacts on the fault dynamic rupture process. In the case of the fault intersecting with ground, the free surface strengthened the rupture. The slip near the surface was obviously increased due to the free surface. And super-shear rupture is easier to occur for the strike-slip fault, while it is impossible for the dip slip fault. However, the effects caused by free surface disappeared when the fault buried deeply into the earth. The varieties of the fault dip angle controlled the rupture propagation as well. With the increase of the dip angle, the slip and slip velocity gradually decreased. It was contributed to the weak coupling between fault and the free surface with increasing dip angle.The homogeneous initial stress and strength distribution caused great changes to the dynamic rupture behaviors. It is easier for the rupture propagated toward the high stress region,which gave a good explanations for the rupture directivity. Along the strike direction, the super shear rupture intends to appear under the control of the high stress. The barrier with high strength hindered or stopped the rupture propagation, which was in accordance with the influences of bend fault with big inclination angle. That is to say, there was a certain equivalent transformation relations between the nonplanar fault geometry and the stress distribution. For the problems in half space, free surface promoted the superposition of the incident wave and reflected wave. Thereby, the wave front energy was enhanced to make the rupture across the barrier. Instead, the rupture behavior in full space was totally different. When the rupture front reached the boundary with high strength, the ceased phase occurred to gradually stop the rupture.The rupture process of the 2010 Yushu Mw7.1 earthquake was reconstructed. And the simulation showed that the super-shear rupture might occur during the whole rupture propagation. The common efforts of free surface and the asperities with high stress could be the most important reasons to the super-shear phenomenon. |
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